Lecture 28: A laboratory model of wind-driven ocean circulation

Transcription

1 Lecture 28: A laboratory model of wind-driven ocean circulation November 16, GFD Lab XIII: Wind-driven ocean gyres It is relatively straightforward to demonstrate the essential mechanism behind wind-driven ocean circulation. The apparatus shown in Fig.1 consists of a rotating perspex disc (to represent the action of the wind) on the surface of a rotating square tank of water with a sloping bottom (to represent, as we shall see, spherical geometry). The stress applied by the lid to the water is analogous to the wind stress at the ocean surface. With clockwise differential rotation of the disc, fluid is drawn inwards in the Ekman layer just under the lid and pumped downwards in to the interior, mimicking the pumping down of water in subtropical gyres by the action of the winds.the varying depth of the tank mimics the variation of the ocean depth measured in the direction parallel to the rotation vector on the sphere see Fig.2. The shallow end of the tank is thus analogous to the poleward side of the ocean basin and the deep end to the tropical side. On introduction of dye to help visualize the flow see Fig.3 we observe a clockwise (anticyclonic) gyre with interior flow moving towards the deep end of the tank ( equatorwards ). This flow (except near the lid) will be independent of depth because the interior flow obeys the Taylor-Proudman theorem. A strong ( northward ) return flow forms at the western boundary; this is the tank s equivalent of the Gulf Stream. We can relate the strength of the north-south flow to the Ekman pumping from under the disc and the slope of the bottom, as follows: w Ek = Dd Dt = Dy d d = v Dt dy dy 1

2 Figure 1: A tank with a false sloping bottom is filled with water so that the water depth varies between 5cm at the shallow end and 15cm at the deep end. A disc is rotated very slowly at the surface of the water in a clockwise sense a rate of 1 rpm works well. To minimize irregularities at the surface, the disc can be submerged so that its upper surface is a millimeter or so underneath the surface. The whole apparatus, disc and all, is then rotated in an anticlockwise sense at a speed of f =10rpm. It is left to settle down for 1/2 hour or so. Holes bored in the rotating disc can be used to inject dye and visualize the circulation beneath. 2

3 Figure 2: (a) An illustration of Taylor-Proudman on a rotating sphere. We consider a spherical shell of homogeneous fluid of constant thickness h. Taylor columns line up parallel to Ω with length d. The latitude is ϕ. (b) A Taylor column in a wedge. If the wedge narrows, or fluidispumpeddownfromthetopatratew Ek, the Taylor column moves sideways to the thicker end of the wedge. This is just how one flicks a lemon seed. The downward motion between finger and thumb generates lateral (shooting) motion as the seed slips sideways. Modified from a discussion by Peter Rhines (1993). 3

4 Figure 3: A time sequence showing the evolution of red dye injected through a hole in the rotating disc. The label N marks the shallow end of the tank. We observe the plume of dye drift southward in the Sverdrup interior where Eq.(??) holds fluid pumped down in to the interior from the disc drives Taylor columns 4 toward the deep end of the tank (southwards). In the bottom picture we see the dye being returned northward in a western boundary current, the laboratory model s analogue of the Gulf Stream or the Kuroshio. Note the east-west asymmetry sketched in Fig.4 southward flow is broad and gentle, northward flow much swifter and confined to a western boundary current.

5 Figure 4: Schematic diagram showing the sense of the wind-driven circulation in the interior and western boundary regions. where now d is the depth of the water in the tank. In our experiment, w Ek ' ms 1 (as estimated for our Ekman experiment, GFD Lab XII above) and the bottom has a slope d = 0.2. Thus v should reach speeds dy of ms 1 or 15 cm or so equatorwards (toward the deep end) in 10 minutes. But the above relation cannot hold over the whole tank because it implies that the flow is southward everywhere draining fluid from the northern end ofthetank. AscanbeseeninFig.3,thewaterreturnsinapolewardflowing western boundary current. But why does the fluidchoosetoreturnonthe western boundary? Why not up the eastern boundary? Let s return to the oceanographic context to see why. 2 Wind-driven gyres and western boundary currents We have seen that wind stresses must drive an equatorward flow in the ocean in the subtropical latitude belt between the midlatitude westerlies and tropical easterlies. Although this flow is indeed observed, we have not yet explained the remainder of the circulation. If we take a very simple view of the geometry of the midlatitude ocean basins (Fig.4), then the equatorward 5

6 flow could be fed at its poleward side by eastward or westward flow, and in turn feed westward or eastward flow at the equatorward edge; either would be consistent with βv = f w Ek, which only dictates the N-S component of the h current. It seems likely that the sense of circulation would mirror the anticyclonic sense of the wind stress, in which case the ocean gyre would be as shown in Fig.(4). Indeed, this must happen since, in reality, the circulation is subject to frictional dissipation (at the bottom and side boundaries, and internally). In order to sustain the circulation, the wind stress must do work on the ocean. Since the rate of doing work is proportional to the product of wind stress and current velocity, these two quantities must, on average, be in phase in order for the work done to be positive. This is the case if the sense of circulation is as depicted in Fig.4, whereas the work done would be negative if, e.g., we closed off the circulation to the east. However, there is still a problem: βv = f w Ek tells us that there is a net equatorward transport h of mass. To ensure continuity there must be flow into and out of the western boundary as shown in Fig.4 and seen in the laboratory experiment, Fig.3; there is an intense western boundary current, within which our assumptions of geostrophy and/or of negligible friction break down. This current is the counterpart in our simple model of the Gulf Stream or the Kuroshio, and other western boundary currents, which are such a striking feature of the ocean circulation; these currents serve to provide a return path for the flow driven equatorward by the wind stress. 6